The thing to remember about the CIWS, is in the automated missile defense mode, it will fire as soon as a target enters it's envelope, and match certain criteria. No human intervention required. This mode, is probably not the smartest mode to be in, with fast gunships zooming around, as the scenario presents itself.
In Manual mode, somebody has to turn a key, and designate a target as hostile. Takes a few seconds longer, but not much longer, and well within that 60 second envelope that has been estimated that they had.
Plenty long enough to detonate the missile at close range, which will still do crippling damage to the ship, but nowhere near the amount, if it had actually struck and detonated.